Kitabı oku: «Fundamental Philosophy, Vol. 2 (of 2)», sayfa 14

CHAPTER III.
UNITY AND SIMPLICITY

16. Real unity and simplicity are identical. What is really one has no distinction in itself; nor is it composed of parts, of which it can be said, this is not that. Evidently simplicity requires nothing more; the simple is opposed to the composite, to what is formed of many beings whereof one is not the other.

17. We meet this simplicity in none of the objects of our intuitions, excepting the acts of our own mind; so that even when we know, by discursion, that there are substances really one or simple, we do not see them in themselves.

Extension consists essentially of parts; whence it happens that we never encounter real unity or simplicity in the corporeal world as object of our sensibility. But as the composite must be resolved into the simple, as it is hard to proceed ad infinitum, we infer that the corporeal universe itself is a union of substances which, whether called points without extension, or any thing else, cannot be decomposed into others; for which reason they are really one, or simple.

18. Hence we conclude that substances may be said to be in a certain manner simple; and that things called composite are unions of substances, which in their turn form a third substance by virtue of a law presiding over them and giving them that unity which we call factitious.

19. We cannot, then, do less than to remark that the transcendental analysis refutes those who deny simplicity to thinking beings, since we have seen that simplicity is prior to composition, which can neither be nor be conceived if it be not presupposed. Simplicity is a necessary law of every being: a composite being ought to be called a union of beings, rather than a being.

20. We have said that simple substances are not objects of our intuition, which has none worthy to be called simple excepting the acts of our mind. The reason of this is, that the principal medium of our intuition is sensibility, which is founded upon representations, themselves based upon extension. There can be no doubt that the acts of our mind, given us by intuition, in the inward sense are perfectly simple; for who can decompose a perception, a judgment, an act of the reason or of the will?

21. The perception of a certain object requires preparatory acts; and the same may be said of judgments and ratiocinations; yet these operations are in themselves exceedingly simple, and cannot be divided into various parts. Simplicity is met with alike in the acts of the will, whether of the pure, intellectual, or sensible will. How shall we divide such acts as these into parts: I desire, I do not desire, I love, I abhor, I suffer, I rejoice?

22. We must take care not to confound the multiplicity of the acts with the acts themselves; there may be many acts, but in themselves they are simple. Thoughts, impressions and affections continually succeed one another in our mind; these phenomena are all distinct from each other, as is proved by their existing at different times, some at one time without the others, and by some being incompatible with others, because contradictory; but each individual phenomenon is by itself incapable of decomposition, and admits in itself no distinction into various parts; wherefore, it is simple.

23. True unity, therefore, is only found in simplicity; where there is no true simplicity, there may be factitious, but not real, unity; since even when there is no separation, there may be distinction between the various parts of which the composite is formed.

24. It may be inferred from this that indistinctum ought, perhaps, to take the place of indivisum in the definition of a one being; because distinction is opposed to unity of identity, and division to union. Absence of division is all that factitious unity requires; but real unity demands that there be no distinction. However closely united two things may be, if one is not the other they are distinct, and cannot, in strict metaphysical language, be called one.

25. The object of these observations is only to fix our ideas, not to modify our language. In common parlance, the idea of unity is used in a less rigorous sense, and, far from opposing this use, we readily accord it a reasonable foundation. There results from the union of two really distinct things, a conjunction, rightly called one so far as it also is subjected to a certain unity; and, were it not permitted to use this word in a sense less rigorous than that exacted by metaphysical analysis, we should be under the necessity of excluding unity from the great mass of objects. Simple substances, we have said, are not offered to us in immediate intuition, and we see compositions rather than their component elements. Could we apply unity only to simple elements, science would be greatly reduced, language would be impoverished, and literature and the fine arts would be despoiled of unity, one of their characteristic perfections.

CHAPTER IV.
ORIGIN OF THE TENDENCY OF OUR MIND TO UNITY

26. Since we encounter multiplicity in all sensible objects, which are those chiefly demanding our attention, how does our mind acquire the idea of unity? In science, in literature, in the arts, and in every thing, we seek unity; and whence this irresistible tendency towards unity, which makes us seek a factitious when we cannot find a real unity, and this, too, notwithstanding the multiplicity presented by all the objects of our perception?

27. Two origins, if we mistake not, may be assigned to this tendency towards unity, the one objective, the other subjective. The former consists in the very character of unity in which the object of the understanding is mainly comprised; the other is the unity found in the intelligent being, and which it experiences in itself. We will explain these ideas more at length.

28. Unity is being; every being is one; and, properly speaking, being is not found without unity. Let us take a composite object: in it we discover two things; the simple component elements of it, and the union of them. The being, properly speaking, does not consist in the union, but in the united elements. The union is a mere relation, not even possible without the elements to be united. On the other hand, these elements in themselves, abstracted from their union, are true beings, existed before, and will exist after their union. What is an organized body? An aggregation of molecules united under a certain law, conformably to a principle presiding over their organization. The parts existed before their organization, and will continue to exist after its destruction. The being, therefore, properly consisted in the elements; and the organization was a relation of them among themselves.

29. Organization requires a principle to rule it, and subject its functions to determinate laws. Thus we see that even relation is subject to unity, to the unity of end and to the unity of a ruling and directing principle.

30. It is inconceivable how the union of distinct things can have any meaning, or lead to any result, if unity do not preside over it. In objects submitted to our experience, things are united in three ways: by juxtaposition in space; by co-existence in time; and by association in the exercise of their activity. The elements constitutive of extension are united in the first way; all objects belonging to the same time, in the second; and in the third all those which unite their forces and direct them to one and the same end.

31. The union consisting in the continuity of elements in space, has no value in the eyes of science, save inasmuch as there is an intelligent being who perceives the forms resulting from this continuity, by reducing them to unity under ideal types. Four lines of points, so disposed as to form a quadrilateral figure, have no scientific meaning until there comes an intelligence and perceives the form of a quadrilateral figure under the aspect of unity. We do not deny that the quadrilateral figure exists independently of intellectual perception: these lines will certainly exist, and be arranged in the same manner, although we prescind all intelligence; but this disposition in the quadrilateral form is a relation, not a being distinct from the aggregation of the elements disposed; and this relation, of itself alone, is no object of intelligence except inasmuch as presented to it under the unity of the quadrilateral form.

The intelligence in search of a true being, can find none, save in elements; and if it wishes to perceive their relation, it must recur to the unity of form.

32. Co-existence in time, is a relation, which, of itself alone, neither gives any thing to, nor takes any thing from objects. These exist independently of this relation; for they must, of necessity, exist, in order to co-exist. This relation denotes something perceptible to the understanding, only as it is presented to it under unity, which, in this case, is unity of time, as in the former it was unity of space.

33. Neither has the association of activities any meaning, except when it expresses the convergence of forces towards one and the same object. If unity be wanting to the point of their direction, their union will express nothing, and the intelligence will have for its object only scattered and unrelated activities.

34. We have then shown that unity is a law of our understanding, founded upon the very nature of things. Absolute being is never found in the composite, but only in the simple, and relative being is not even conceivable, if it be not submitted to unity.

35. We discover in the very nature of our mind, the second origin of its tendency to unity. It in itself is one, is simple, and therefore disposed to assimilate every thing to itself under this same unity and simplicity. It feels that it is one in the midst of multiplicity, permanent even in succession, and under all the immense variety of sensible phenomena, intellectual and moral, which it unceasingly experiences. The inward sense attests with irresistible certainty the identity of the me. This unity, this identity, is as certain, as evident to the child who begins to feel pleasure or pain, and is sure that he is one and the same that experiences both impressions, as they are to the philosopher who has spent long years in profoundly investigating the idea of the me and the unity of consciousness.

The unity and simplicity which we experience in ourselves force us to reduce the composite to the simple, the multiple to the one. The perception of things the most composite refers to a consciousness essentially one: even were we to perceive the whole complicated universe by a single act, this act would be most simple, since otherwise the me could not say, I perceive.

36. Two reasons, then, exist why our mind in all things seeks unity. Objects are unintelligible, except so far as subjected to a certain perceptible unity, to a form, under which the multiple is made one, and the composite simple. The object of the understanding is being, and being consists in the simple. The composite involves an aggregation of simple elements with the relation called union; but unless this be presented under a certain unity, it does not constitute a perceptible object.

Without the indivisible unity of consciousness, no intelligent subject is conceivable. Every intelligent being requires this link to unite the variety of phenomena of which it is the subject. If this unity fail, the phenomena become an informal aggregation, unrelated among themselves: intellectual acts without an intelligent being.

The tendency to unity originates in the perfection of our mind, and is itself a perfection; but it needs to be carefully watched, lest it go astray, and seek real unity there, where only a factitious unity can be found. This exaggeration is the cause of pantheism, the fatal error of our day. Our mind is one, so also is the infinite essence, cause of all finite beings; but the aggregation of these beings is not one, for even when united by many ties, they cease not to be distinct. There is in the world unity of order, of harmony, of origin, and of end; but there is no absolute unity. Number also enters into unity of harmony, but it is incompatible with absolute unity, as reason and experience both show.

CHAPTER V.
GENERATION OF THE IDEA OF NUMBER

37. Unity is the first element of number, but does not of itself alone constitute number, which is not unity, but the collection of unities.

38. Two is a number. What is our idea of the number two? Evidently it is not confounded with its sign, for signs are many and very different, but it is one and always the same.

39. It would seem at first sight that the idea of two is independent of the mode of its generation, and that, being one, it may be formed by addition or subtraction, by adding one to one, or taking one from three: 1 + 1 = 2; 3 – 1 = 2. But if we reflect upon these two expressions, we shall see that the latter is impossible without the former. We should not know that 3 -1 = 2 if we did not previously know that two entered into the composition of three, and how it entered. We could know nothing of this had we not already the idea of two, and this idea is nothing else than the perception of this sum.

40. The idea of two is no sensation, for it extends alike to the sensible and the non-sensible, to the simultaneous and the successive. In itself it is simple, its object is composite.

41. Since the collection of objects is small in two, the imagination can easily figure to itself what the understanding perceives; and the idea seems clearer to us because made sensible by a representation. The idea of addition made, in facto, that is, the idea of the sum, enters into that of two, but not of addition in fieri. Our idea of this number is perfectly clear, and yet we do not continually think of one plus one.

42. The idea of two refers to the simultaneous as well as to the successive; but our mind does not discover it until after it has the idea of succession. The object of this perception is the relation of united things; the understanding perceives them as such, and then only has it the idea of two.

43. Neither the successive nor simultaneous perception of two objects unaccompanied by relation is the idea of two. Hence the saying: a man and a horse do not make two, but only one and one; and the reason of this is that the man and the horse are represented to the understanding by their difference, not by their resemblance; and things must be presented to the mind under a common idea in order to give number. Thus, if we abstract their difference, and consider them only as animals, or corporeal beings, or beings simply, or things, they will make two.

44. In objects, then, totally unlike, or not comprehended under some common idea, there can be no number. Abstract number is number by excellence; because it eliminates all that distinguishes the things numbered, and considers them only as beings, consequently as similar, as contained in the general idea of being. Concrete numbers are only numbers so far as they participate in this property. Two is applicable to one horse and another horse, but not to a horse and a man, unless we identify them under the idea of animal, and abstract rationality and irrationality. Concrete number requires a common denomination; otherwise it is not number.

45. The idea of distinction, that is, that the one is not the other, enters into the idea of two, so that this idea necessarily involves an affirmation and a negation. The affirmation is of the real, possible, or imaginary existence of the things counted; the negation is of the one with respect to the other. Affirmation without distinction or negation involves identity. The idea of two, as well as that of every other number, includes the ideas of identity and distinction. The identity is of each extreme with itself; the distinction is of the extremes among themselves. Identity in the thing is the thing itself: identity in the idea is the simple perception of the thing. Distinction in the thing is the negation of it with respect to others: distinction in the idea is the perception of negation. We always perceive a thing as identical, and consequently every perception includes the idea of unity. But we do not always, when we perceive a thing, observe its negation with respect to others, and consequently do not always perceive number. The idea of number originates in comparison, when we see an object which is not another.

46. The ideas of being, distinction, and similarity enter into that of two. The idea of being, because nothing cannot be counted: that of distinction, or negation of the one being the other, because the identical does not constitute number: that of similarity, because things are only numbered when abstraction is made of their difference. Being is the basis of perception; distinction, of comparison; and similarity, of union. Perception begins with unity, proceeds with distinction, and ends with similarity, which is a kind of unity. The perception of this similarity unites what is distinct; but the union need not always be of the things, but may be in the idea comprising them. There are two poles of the world, but they are not united. The perception of the number two requires something more than the simple perception of objects; they must be susceptible of comparison, and consequently united in a common idea. This perception, therefore, demands comparison and abstraction, and this is why animals cannot numerate; they can neither compare nor generalize.

47. The analysis of the idea of two is the analysis of all numbers; the difference is not of nature, but of more and less; in the repetition of the same perception.

48. If any one now ask whether number be in the things, or in the mind alone, we reply that it is in things as in its foundation, because both distinction and similarity are in the things; that is, the one is not the other, and both have something in common; but it is the mind that sees all this.

49. After having perceived the distinction and union of two objects, we can also perceive another object, which will be neither the one nor the other of them, and will yet be comprehended in one general idea with them. This is the perception or idea of the number three. No matter how many numbers be imagined, nothing will ever be discovered in any of them except a simultaneous perception of objects, distinction of objects, and similarity of objects. If these be determinate, we shall have concrete number; if they be comprised in the general idea of being, of thing, we shall have abstract number.

50. The limits of our mind prevent it from comparing many objects at one time, and from easily recollecting the comparisons it has already made. To assist the memory, and the perception of these relations, we make use of signs. When we pass beyond three or four, our power of simultaneous perception fails, and we divide the object into groups which serve us as new units, and are expressed by signs. Ten is clearly the general group in the decimal system; but before we reach the number ten we have already formed other subalternate groups; since to count ten, we do not say one and one and one, etc., but one and one, two; two and one, three; three and one, four, etc. Each unit added forms a new group, which, in its turn, serves to form another. With two, we form three; with three, four, and so on. This affords an idea of the relation of numbers with their signs; but, as this matter is too important to be here dismissed, we will further develop it in the following chapters.

CHAPTER VI.
CONNECTION OF THE IDEAS OF NUMBER WITH THEIR SIGNS

51. The connection of ideas and impressions, in a sign, is a most wonderful intellectual phenomenon, and at the same time of the greatest help to our mind. Were it not for this connection, we could scarcely reflect at all upon objects somewhat complex, and above all our memory would be exceedingly limited.²⁶

52. Condillac made some excellent remarks upon this matter: in his opinion, we cannot, unaided by signs, count more than three or four. If, indeed, we had no sign but that of unity, we could readily count two, saying one and one. Having only two ideas, we could easily satisfy ourselves that we had twice repeated one. But it is not so easy to be certain of the exactness of our repetition when we have to count three, by saying one and one and one; still, this is not difficult. It is more so to count four, and next to impossible to go as far as ten. If we undertake to abstract the signs, we shall find that it is impossible to form an idea of ten by repeating one; and that it will be alike impossible, if we employ no sign, to make sure that we have repeated one exactly ten times.

53. Suppose the sign two, and one half of the difficulty is obviated; thus it will be much easier to say two and one, than one and one and one. In this supposition four will be no more difficult than was two, since, just as we before said, one and one, two; we now say, two and two, four. The attention before divided four times by the repetition of one, is now only divided twice. Six was before a hard number to count, but, in the present supposition, it is as easy as three was before; for, if we repeat two and two and two, we shall have six. The attention before distracted by six signs, is now distracted only by three. Evidently, if we continue to form the numbers three, four, and so on, expressive of distinct collections, we shall gradually facilitate numeration, until we attain the decimal simplicity now in use.

54. It may here be asked if the actual system be the most perfect possible? And if facility depend upon the distribution of collections in signs, can there be any thing more perfect than this distribution? Either there is question of new signs to denote new collections, or of the combination of signs. There can be no number which we cannot express with our present system, and consequently there is no need of inventing any thing to denote new collections. New signs might perhaps be invented for these collections, and these collections might possibly be distributed in a simpler and more convenient manner. In this case we admit an amelioration to be possible, though very difficult; but none in the former. In a word, the only possible progress would be in expressing better, not in expressing more.

55. The sign connects many ideas which, without it, would be isolated; hence its necessity in many cases, its utility in all cases. With the word hundred, or its numerical representative, 100, we know that we have one repeated a hundred times. Were this help to fail, we could not speak of a hundred, base calculations upon it, or even form it. It is, however, well said that we do not succeed in forming it except by tens, by repeating the calculation ten ten times.

56. Let it not, therefore, be thought that the idea of the number is the idea of the sign; for evidently the same idea of ten corresponds to the word ten, whether written, spoken, or numerically represented by the figures 10, although these three signs are very different. Every language has a word of its own to express ten, and all people have the same idea of it.

57. This last remark creates a difficulty as to what the idea of ten consists in. We cannot say that it is the recollection of the repetition of one ten times; first, because we do not think of this recollection when thinking of ten; and second, because, according to what has already been said, a clear recollection of this repetition is impossible. Neither is it the idea of the sign, for the idea signified existed before the sign was invented, otherwise the invention would have had no object, and would even have been impossible. There can be no sign where there is nothing to signify.

The idea of number includes more difficulties than Condillac ever imagined; who, if he had, after his close analysis of what facilitates numeration, profoundly meditated upon the idea itself, would not so readily have censured St. Augustine, Malebranche, and the whole Platonic school, for having said that numbers perceived by the pure understanding are something superior to those perceived by the senses.